Some divisibility results for the cyclotomic class number

Rok, strany: 1997, 59 - 68

Let $p$ and $q$ be odd primes such that $p= 2q+1$. It is known (D. Estes 1989) [D. Estes: On the parity of the class number of the field of $q$th roots of unity, Rocky Mountain J. Math. 19 (1989), 675–682] that the class number of the $p$th cyclotomic field is odd if the prime 2 is inert in the maximal real subfield of the $q$th cyclotomic field. We show how this result follows from an elementary character sum identity. By a similar argument we also prove some other divisibility results for this class number.

ISO 690:

Mätsänkylä, T. 1997. Some divisibility results for the cyclotomic class number. In Tatra Mountains Mathematical Publications, vol. 11, no.2, pp. 59-68. 1210-3195.

APA:

Mätsänkylä, T. (1997). Some divisibility results for the cyclotomic class number. Tatra Mountains Mathematical Publications, 11(2), 59-68. 1210-3195.